Question

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork ?

• A. 335Hz
• B. 338Hz
• C. 345Hz
• D. 342Hz

Answer 1

Answer: (A)

335Hz

Answer 2

Let the frequency of tuning fork A be $f_A$ and the frequency of the known tuning fork be $f_B$. We are given $f_B = 340$ Hz.

The initial beat frequency is given as 5 beats/s. The beat frequency is the absolute difference between the frequencies of the two tuning forks. So, $|f_A - f_B| = 5$. This gives two possibilities for the frequency of fork A:

1. $f_A - 340 = 5 \implies f_A = 340 + 5 = 345$ Hz
2. $f_A - 340 = -5 \implies f_A = 340 - 5 = 335$ Hz

When fork A is filed, its frequency increases. Let the new frequency of fork A after filing be $f_A'$. The new beat frequency with the known fork B is 2 Hz, so $|f_A' - 340| = 2$. This gives two possibilities for the new frequency of fork A:

1. $f_A' - 340 = 2 \implies f_A' = 340 + 2 = 342$ Hz
2. $f_A' - 340 = -2 \implies f_A' = 340 - 2 = 338$ Hz

Since filing increases the frequency, $f_A' > f_A$. If the initial frequency was 345 Hz, the frequency would have to increase to either 342 Hz or 338 Hz, which is impossible. If the initial frequency was 335 Hz, the frequency would have to increase to either 342 Hz or 338 Hz, which is possible.

Therefore, the original frequency of fork A must be 335 Hz.